Models of atomic scale contrast in dissipation images of binary ionic surfaces in non-contact atomic force microscopy

Computational model for noncontact atomic force microscopy: energy dissipation of cantilever

We propose a computational model for noncontact atomic force microscopy (AFM) in which the atomic force between the cantilever tip and the surface is calculated using a molecular dynamics method, and the macroscopic motion of the cantilever is modeled by an oscillating spring. The movement of atoms in the tip and surface is connected with the oscillating spring using a recently developed coupling method. In this computational model, the oscillation energy is dissipated, as observed in AFM experiments. We attribute this dissipation to the hysteresis and nonconservative properties of the interatomic force that acts between the atoms in the tip and sample surface. The dissipation rate strongly depends on the parameters used in the computational model.

Coupled molecular and cantilever dynamics model for frequency-modulated atomic force microscopy

A molecular dynamics model is presented, which adds harmonic potentials to the atomic interactions to mimic the elastic properties of an AFM cantilever. It gives new insight into the correlation between the experimentally monitored frequency shift and cantilever damping due to the interaction between tip atoms and scanned surface. Applying the model to ionic crystals with rock salt structure two damping mechanisms are investigated, which occur separately or simultaneously depending on the tip position. These mechanisms are adhesion hysteresis on the one hand and lateral excitations of the cantilever on the other. We find that the short range Lennard-Jones part of the atomic interaction alone is sufficient for changing the predominant mechanism. When the long range ionic interaction is switched off, the two damping mechanisms occur with a completely different pattern, which is explained by the energy landscape for the apex atom of the tip. In this case the adhesion hysteresis is always associated with a distinct lateral displacement of the tip. It is shown how this may lead to a systematic shift between the periodic patterns obtained from the frequency and from the damping signal, respectively.

Complex design of dissipation signals in non-contact atomic force microscopy

Complex interplay between topography and dissipation signals in Non-Contact Atomic Force Microscopy (NC-AFM) is studied by a combination of state-of-the-art theory and experiment applied to the Si(001) surface prone to instabilities. Considering a wide range of tip-sample separations down to the near-contact regime and several tip models, both stiff and more flexible, a sophisticated architecture of hysteresis loops in the simulated tip force-distance curves is revealed. At small tip-surface distances the dissipation was found to be comprised of two related contributions due to both the surface and tip. These are accompanied by the corresponding surface and tip distortion approach-retraction dynamics. Qualitative conclusions drawn from the theoretical simulations such as large dissipation signals (>1.0 eV) and a step-like dissipation dependent on the tip-surface distance are broadly supported by the experimental observations. In view of the obtained results we also discuss the reproducibility of NC-AFM imaging.

Understanding dissipative tip-molecule interactions with submolecular resolution on an organic adsorbate

Three-dimensional force spectroscopy measurements on 3,4,9,10-perylene-tetra-carboxylic dianhydride adsorbed on Ag(111) are combined with first-principles calculations to characterize the dissipative tip-molecule interactions with submolecular resolution. The experiments reveal systematic differences between the energy dissipation at the end groups and the center of the molecules that change with the tip-sample distance. Guided by the strength of the experimental conservative forces, an Ag-contaminated Si tip is identified as the likely tip termination in the experiments. Based on this tip configuration, the energy dissipation in the tip-sample contact is determined from the approach and retraction force curves calculated as a function of distance for different molecule sites. These calculations provide an explanation for the experimental trends in terms of the competition between localized dissipation mechanisms involving the quite mobile oxygen atoms on the sides of the molecule, and global molecular deformations involving the more rigid perylene core. The results confirm that the observed dissipation can be explained in terms of adhesion hysteresis and show the power of combined experimental-theoretical spectroscopy studies in the characterization of the underlying microscopic mechanisms.

Models of the interaction of metal tips with insulating surfaces

We present the results of atomistic simulations of metallic atomic-force-microscopy tips interacting with ionic substrates, with atomic resolution. Chromium and tungsten tips are used to image the NaCl(001) and MgO(001) surfaces. The interaction of the tips with the surface is simulated by using density-functional-theory calculations employing a mixed Gaussian and plane-wave basis and cluster-tip models. In each case, the apex of the metal cluster interacts more attractively with anions in the surfaces than with cations, over the range of typical imaging distances, which leads to these sites being imaged as raised features (bright) in constant-frequency-shift images. We compare the results of the interaction of a chromium tip with the NaCl surface, with calculations employing exclusively plane-wave basis sets and a fully periodic tip model, and demonstrate that the electronic structure of the tip model employed can have a significant quantitative effect on calculated forces when the tip and surface are clearly separated.

The role of the tip in non-contact atomic force microscopy dissipation images of ionic surfaces

In this paper we use simulations to investigate the role of the tip in nc-AFM measurements of dissipated energy. Using a virtual AFM we simulate the experiment focusing on the atomic scale energy dissipation on an NaCl(100) flat surface. The non-conservative interaction was treated with the theory of dynamic response and all the calculations were carried out using an atomistic model; several sets of tips were tested using ionic crystals (NaCl, KBr, MgO), each in different configurations (ideal, vacant, divacant, doped). Using an MgO-doped tip we were able to calculate a dissipation signal comparable to what is typically measured in experiments. It was not possible to see any dissipation with ideal tips, although they still have a significant interaction with the surface and give atomic contrast in the frequency shift signal. The effect of the scanning speed on measured frequency shift and dissipation is also calculated and discussed.

Temperature dependence of energy dissipation on NaCl(001) in non-contact atomic force microscopy

The dissipative tip-sample interactions are measured by dynamic force spectroscopy for silicon tips on NaCl(001) in ultrahigh vacuum in the attractive and repulsive force regimes. Force and dissipation versus distance curves were obtained for different sample temperatures ranging from 35 to 285 K. Detailed comparison in different distance regimes shows that neither the force nor energy dissipation exhibits a systematic variation with sample temperature.

Modelling the manipulation of C60 on the Si001 surface performed with NC-AFM

We present a theoretical model of manipulation of the C(60) molecule on the Si(001) surface with a non-contact atomic force microscope (NC-AFM). The model relies on the lowering of the energy barrier for the C(60) manipulation due to the interaction of the C(60) with an AFM tip and the subsequent thermal movement of the molecule over this barrier. We performed numerical simulations of these energy barriers for a series of tip positions relative to the molecule to show how the barriers change with the tip position. The values of these barriers are then used in kinetic Monte Carlo simulations to estimate the probability of the C(60) movement for different tip positions and temperatures. Virtual atomic force microscope simulations, which include the kinetic Monte Carlo treatment of the C(60) movement, are then performed to describe in real time the process of movement of the C(60) molecule during an NC-AFM scan. Our results demonstrate that manipulation of the C(60) molecule, which is covalently bound to the surface, is possible with NC-AFM, even though there is no continuous tip-molecule contact, which is known to be a necessary requirement for the C(60) manipulation with scanning tunnelling microscopy. We show that the manipulation event can be identified in real NC-AFM experiments as an abrupt change in the distance of the tip closest approach (topography), and as spikes in the frequency shift and dissipation signals.

Ubiquitous mechanisms of energy dissipation in noncontact atomic force microscopy

Atomistic simulations considering larger tip structures than hitherto assumed reveal novel dissipation mechanisms in noncontact atomic force microscopy. The potential energy surfaces of realistic silicon tips exhibit many energetically close local minima that correspond to different structures. Most of them easily deform, thus causing dissipation arising from hysteresis in force versus distance characteristics. Furthermore, saddle points which connect local minima can suddenly switch to connect different minima. Configurations driven into metastability by the tip motion can thus suddenly access lower energy structures when thermal activation becomes allowed within the time required to detect the resulting average dissipation.

Mechanical manifestations of rare atomic jumps in dynamic force microscopy

The resonance frequency and the excitation amplitude of a silicon cantilever have been measured as a function of distance to a cleaved KBr(001) surface with a low-temperature scanning force microscope (SFM) in ultrahigh vacuum. We identify two regimes of tip-sample distances. Above a site-dependent critical tip-sample distance reproducible data with low noise and no interaction-induced energy dissipation are measured. In this regime reproducible SFM images can be recorded. At closer tip-sample distances, above two distinct atomic sites, the frequency values jump between two limiting curves on a timescale of tens of milliseconds. Furthermore, additional energy dissipation occurs wherever jumps are observed. We attribute both phenomena to rarely occurring changes in the tip apex configuration which are affected by short-range interactions with the sample. Their respective magnitudes are related to each other. A specific candidate two-level system is also proposed.